In applying the ultrasonic contrapropagation method to the measurement of flow in highly attenuating fluids, or to fluids in conduits having only limited access, it is sometimes necessary to interrogate along a path other than the conventional tilted diameter or midradius chordal paths. The meter factor K, which relates the path average to the area-averaged flow velocity, is derived from Nikuradse profiles for several new paths. The results enable one to locate transducers so that for the chosen type of path, K will be (a) minimally dependent on Re, and/or (b) approximately equal to unity, or (c) represented by a simple function of Re. For smooth-wall steady flow conditions, the error in the calculated K’s is estimated as ±2 percent ± the effect due to the disturbance of Nikuradse profiles by the transducers.

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